Method of and means for frequency stabilizing signal generators



L. E. NORTON METHOD OF AND MEANS FOR FREQUENCY STABILIZING SIGNAL GENERATORS Aug. 23, 1949.

3 Sheets-Sheet 1 Filed Feb. 26, 1945 L. E. NORTON METHOD OF AND MEANS FOR FREQUENCY Aug. 23, 1949.

STABILIZING SIGNAL GENERATORS 5 Sheets-Sheet 2 Filed Feb. 26, 1945 NEMWN u i .n t

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Aug. 23, 1949. 1.. E. NORTON ,4

METHOD OF AND MEANS FOR FREQUENCY STABILIZING' SIGNAL GENERATORS Filed .Feb. 26, 1945 3 Sheets-Sheet 3 F i Egg/a 7 a 34., 22 I 3%??32 z w =E i 2x Patented Aug. 23, 1949 METHOD OF AND MEANS FOR'FREQUENCY STABELIZING SIGNAL GENERATORS Lowell E Norton Princeton Junction, N. J as- .signorto Radio Corporation of America, a corporation of Delaware Application February 26, 1945, Serial No. 579,766 17 Claims. (Cl.-250-36) This invention relates generally to signal generating systemsand more particularly to improved methods of and means for stabilizing the frequency of signal enerating systems by means oi i control resonator networks.

1.;Q1OS8 frequencycontrolof magnetrons or other ultra-high frequency generators has become of increasing importance. due tothe widespread use ofSU-ch devices assourcesof ultra-high frequency energy, Frequency stabilization is particularly necessary when the magnetron or other high frequeney. source mustoperate-unattended for comparatively longintervalsdurin-g which ambient temperatures, terminal impedances, operating potentials and currents and magnetic field characteristics may fluctuate or vary between wide limits.

,The.methods of and,means;for frequency stabilizing such devices to .be described in detail hereinafter, may-be employed at any frequency. They are particularly convenient. when the frequency is sufficientlyhigh so that the use of waveguide or transmission linesections having distributed reactance characteristics are feasible. At lower frequencies, artificiallines comprising lumped circuit components may be substituted for lines having distributed constants. At any frequency, equivalent ,circuits comprising combinations of suitable mutualreactances, lumped or I distributed reactances and resistances, may be employed..,

It is well known t-hat agenerator- Whichineludes .two resonant circuits having relatively widely differing Q values will .be .controlledby the: resonant circuit li ayin'gthe higher Q value, and effectively controlled if, the higher fQ cire cuit has the lower resonant resistance. It also is well known that other parameters being equal, higher Q71 resonant circuits, provide improved frequency stability .in. such generators.

Heretofore, high frequency oscillators and magnetrons have been frequency-stabilized (a) by paralleleconnecting ahigh Q controlresonator with the load and generatoror, (b). bY-D connecting a high Q control resonatorwhich is transformedto a lower resultant impedance in an intermediate stage, said transformed resonant circuit being shunt-connected with the load and oscillator. The relative advantages of these systems are discussed in greater detail hereinafter. However, they both have inherent limitations which preventthe high degree of frequency stability necessary for many high frequency signal transmissiomsystems.

The instant invention provides improved fre- 2 I quency stability over that attainable'with prior systems, and although somewhat unorthodox in theory and application, it is readily adaptable to thefrequency stabilization of signal generators at any freuqency. The frequency stabilizing network comprises a high Q impedance of a complexnaturewhich is transformed to a newirnpedance with a higher Q and lower absolute value, and which is then parallel-resonated with another reactance of opposite sign. Thesynthetic control resonator thusprovided is parallel-connectedv to the generator and load to stabilize the frequency of the generator.

Circuit elements. having rapid rates of change ofphaseanglewith frequency and critical optimum line lengths maybe determined, as described in detail hereinaften-to provide practical circuit configurations. t is emphasized that the instant, system differs from previous practice wherein the. reactive elements of a high Q resonator arefirst combined, and then transformed to new-values, thetransformed resonator impedance being shunt-connected with the generator and load. 1

Use of the instant invention has been found to v provide frequency stability of one partin twenty thousand at 10,000.megacycles per second for changes in ambient temperatures of 5010. It also provides frequency stabilization to one part'of twenty thousand for 3:1 changes in magnetron current ina magnetron generator. Furthermore, the system is effective in reducing frequency shifts due to variations in load impedance. For any terminal impedance of random phase andv magnitude which will provide a standing wave ratioof notmore than 1.5 in a waveguide system connecting the load and the stabilizer system, it is possible to limit the frequency shift to one part in fifteen thousand over the entire range of terminalv impedances represented by these conditions. The improved operation is due to the fact that the theoretical limit of the resultant effective of the conrol impedance may be shown to be one half of the squared value c) of the of the control impedance. The limiting factor is the loss in the impedance transformation.

Among the objects of the invention are to provide improved methods-of and means for stabilizing the output frequency of signal generators. Another object is to provide improved methods of and means forsynthesizing control resonant circuits for stabilizing frequency generators. An additional object of the invention is to provide improved methods of and means for synthesizing a high Q resonant circuit. A further object is to provide improved methods of and means for effectively raising the Q of a resonant circuit Another object is to provide improved methods of and means for frequency-stabilizing signal generators for variations in ambient temperature, operating voltages and currents, and variations in terminal impedance. A still further object of the invention is to provide improved methods of and means for providing a high Q resonant circuit wherein a high Q impedance is transformed to a lower impedance value having a higher Q, and then said transformed impedance is parallel-resonated with a reactance of opposite sign.

The prior art and the instant invention, both as to theory and practical circuit configurations, will be described in greater detail by reference to the accompanying drawings of which Figures 1 to 13 are schematic circuit diagrams illustrating the mathematical discussion of the features of the invention, Figure 14 is a graph illustrating said mathematical treatment of the invention, Figure 15 is a fragmentary perspective view of the coupling between the generator and the stabilizing network, Figure 16 is a side elevational view of a first embodiment of the invention,

Figure 17 is a cross-sectional end elevational view of said first embodiment of the invention taken along the section line XVII, and Figure 18 is a perspective view of a second and preferred embodiment of the invention. Similar reference venience may be expressed in terms of impedance concepts. The resulting equivalent circuits may contain many elements which may or may not be linear with certain parameters such as frequency. However, under any one set of operating conditions, this complicated equivalent circuit may always be replaced by a characteristicless potential, e, which is independent of frequency or external impedances, and a single impedance, Zint, as shown in Figure 1. If the operating parameters are changed even slightly it is possible for the new, simple equivalent circuit to contain a radically different potential and impedance.

The generator I, may be considered as having load terminals t3 and t4. It would be advantageous to have terminals t1 and 152 available, but terminals t3 and ii are the only ones which are accessible. However, if Zint is of the form it will always be possible, by proper choice of an external circuit, to tune out the reactive term with an external series reactance ZCext which is Zint=Tint+i$int 4 terminals t3t4 no longer depends upon the actual circuit configuration.

Actually a circuit with this limitation is of no value since by specifying that the elements are all reactive, it is assumed that the system will not be allowed to radiate or to supply power to a load. To be useful, at least one of the impedances of the external circuit must be complex and therefore contain a real term. By introducing only one real term in the external circuit of Figure 2 the actual circuit configuration becomes important since the rate of phase change, with frequency, at terminals t3t4 will depend upon the particular configuration.

If Zmt, is controllable, then it must be so chosen that a large rate of phase change with frequency at t3t4 will also produce a large rate of phase change at 151-452. If there is no control of mint, then the external circuit must produce a large rate of phase change with frequency at t1tz and not necessarily at t3t4.

One other practical restriction must be imposed on the external circuits. At very high frequencies it is difficult to measure impedances and other quantities related to potentials and currents in composite circuits. Therefore, the final circuit must not be so complex as to preclude the possibility of accurate adjustments of the circuit elements. Also, if possible, critical and radical changes in circuit operation which will be easily detectable in monitoring equipment used during adjustment should occur near optimum adjustment of critical circuit values, so that proper initial adjustment may be made.

Obviously, an infinite number of circuit configurations is possible. To insure a correct approach to the problem without becoming quite hopelessly involved in too many possible circuit forms, it is desirable to make certain reasonable approximations which transform the problem to a much simpler one. The validity of these initial approximations may be examined when a tentative stabilizing network has been found.

, COMPARISON OF FREQUENCY STABILIZA- a certain inherent frequency stability so that Zlnt may be defined in terms of [Zeal and an equivalent Q. The elements which determine this Q may be actual physical elements or equavalent elements which may be due, for example, to electron beam loading of resonators.

Let the Q of the oscillator i be Q3, and the parallel impedance associated with the Q3 be To observe the impedance-frequency characteristics of this parallel resonant circuit, it is convenient to use the simple arrangement of Figure 3. Let the frequency change from f to f(1+6) where 5 1. The reactances in Figure 3b have values .223 and we at 6:0.

Then

This reduces to $3 is expressediinterrns of theother parameters and at any frequency Then, since only the cases where.Q ,1an d where 6 1 are of interest 3Q3[ Q3] oaand in Figure 3a aQa 1 +4Q 5 2Z3Q325 Q3 Another external resonator having a Q of Q2 and impedance is to be connected in parallel with the fii s't resonator. The resulting parallel impedance is a (R22 $22) '1' R2 (R32 2 "1' 4 0 Z Z2Z3 2( 3 3 +$3(R22+$22)] 4 Z2+Z3 2+ a) 2+ s) for the impedance branches, and

-z5=w.= fj; (13

for the reactance branches.

By definition 2 R2-Q2 (1,4) and EL R3Q3 .3

and t0 3 1 then Equation 13 reduces to 3 Z5--$D x3+x2 to a Veryclose degree of approximation. Actually then the single equivalent parallel circuit is obtained by connecting Z4 and Z5 in parallel. However, since :63 and 302' have beentaken vas pure imaginaries, the Q of the resultant equivalent circuit is determined only by Z4-with its associated Q4.

:From (14) The'quantity /a:2?:-|-R is the impedance 'a'sso- 'ciated with *the external control resonator, and '-/m +R'3 is th'e impedance associated'with the escinatsr.

fF'roin Equations 18, '19,--"and 20 R z z 2 1 R3 Q 211 k R32 -Q22+ 1 or R2-7 (21) From Equation 21 and Equation 14 no. Q 2Y1 932=R2Q2 i 2 QZLFI From Equation 12 and Equation 20 Z4 2 2 2 3 z) i 3 2 1 (23) 2%:Re')' z+:vi) and by definition the equivalent Q associated with Z; is

Q4 which is the'Q resulting whenzclrcuits of Qzland Q3 are connected in parallel.

From Equation 15, :Equation 21, -11."qua tion :22 and Equation 24.

Q"+mQ w/ Q Q2' +.1 I Q3 +-l.

1+m Q22+1 For any stabilizing work "off interestfQg 1. Also, nn'rortiinatem, Q3 1. For this "situation Equa: ti'on '25 reduces to Q2 If P is a number relating Q2 and Q3 so that 'i P- Q3 thatis, P-is the ratio-'of the control Q to the oscillator Qth en Equation 26 reduces to Q4 1 3 and also QFQZZ' E (29 The parallel impedance obtained by paralleling Z4 and Z5 is Z223 $3272 Z2+ a s-l z in which Z2=R2+i322 and Z3'=R3-|i333. The reactances 0:2 and x3 are functions ofrfrequencygj. As is always the case, the resonant resistance of 24-5 is Therefore this parallel resonator type of control will not be very satisfactory in most cases. The external resonator Q which is Q2, will be that obtained from a good cavity and may, for example, be about 5000. If it is assumed that there is very little external loading on the external resonator and slight loadingon the oscillator resonator other than electronic loading of the cavity, then the factor 172 is almost certain to be less than unity since the oscillator resonator must have a lower Q than the external resonator. Probably the best that may be hoped for is the condition Using this result in Equation 28 and assuming that it is possible to build an external control cavity such that Apparently, therefore, the best result which can be obtained from such a simple arrangement is an improvement of about two to one.

Actually, when the practical case is considered which involves power dissipation in a terminal impedance, the situation is even less favorable. The increased frequency stability indicated in Equation 28 is obtained by attaching an external high Q resonator. It is likely that the parallel resonant resistance of the combination will be very high. The external load must be transformed to a high value to avoid excessive shunting of the resonators. This in itself is not too easy to accomplish at the higher frequencies. In addition the overall high impedance circuit will be shunted excessively by stray impedances which are almost always present in any circuit.

METHOD IIRESONATORS PARALLEL-CDUPLED THROUGH A TRANSFORMER where it is assumed that The resultant Q and impedance of this transformed resonator connected in parallel with the oscillator resonator can be expressed easily. Let the parallel impedance be Z4==Ri'+ir4' and the parallel Q be Q4. It is convenient to use Figure 8. 3 again as the equivalent except that a, R3, and we becomes 0:2, R2, and an" respectively where As before, if

then ri -4:2". If Z4 is composed of Z2 and Z3 in parallel, then If, as before in Equation 32 and Equation 33, it is assumed that m=1 is the best obtainable value, P=10, and that it is possible to make s=10 then, from Equation 43 This represents an improvement of l /2:1 as compared to the original improvement of about 2:1. The circuit will have lower impedance values than the untransformed version of Method I, so that unavoidable shunt impedances will be less objectionable, and the load impedance transformation will be less diflicult since the required ratio is lower.

Mnrrron IIICONTROL IMPEDANCE TRANSFORMED, RESONATED AND SHUNT-CONNECTED 'ro GENERATOR By resorting to an entirely different circuit principle of frequency stabilization much greater improvement is obtainable. The basic circuit of the instant invention is shown in Figure 4. The impedance Z1 will be the parallel impedance of the two branches in the plane A-A. The lines are of length L1 and L2 and may be either wave guides, transmission lines, artificial lines, or equivalent circuits containing mutual reactances and impedances.

Referring to Figure 4, it is convenient to let the characteristic impedances of lines L and L1 be alike and represented by Zr, and the propagation constant P='a+i;3.

Actually, of course, the lines will have some attenuation so that transmission equations will in general have exponential attenuating factors, and the line equations may be written conveniently with the use of the usual hyperbolic functions. However, to simplify the expressions greatly, it may be assumed that the distributed series resistance of the line per unit length approaches zero and the distributed shunt resistamass- 2 9" 1O ance-of theline perun-it length approaches intoo high. The attendant ditficulties for a high finity. Thus the hyperbolic functions may be reresonant resistance have already been discussed.

placed by their corresponding trigonometric The result is that the Qof the branch R+izv will functions. Accordingly, the impedance Z1 in the be limited quite severely.

plane A--A is If a line length L is selected which will trans- Rg-k cos ,cLi-i sin [3L cos BL +i sin BL cos {EL-H sin 6L cos flL zj sin 5L Z1=ZkR%kix cos BL-H sin 6L cos BL +isin 6L cos BL+i Zj sin BL cos [3L +'L sin (3L Rationalizing, an exceedingly cumbersome exform the impedance Z=R+i t z =R +im i pression for Z1 is obtained, which may be written which iii-simplified form 1); (l7 r Z1 +z (45a) and R, R (48) in which p and p' are each functions of R, :0, R6, R +x Rfi-l-a Zk, B and fi the impedance |Z[ can be transformed to a small The various circuit constants must be selected numerical Value. and related so that the maximum rate "of phase ratio I ti and at the same tune the change with frequency in Z1 at A-A is obtained.

This may be accomplished by making Ra I NC?) is transformed to alarger ratio 6R2 =0 for a maximum (46a) so 3& l 520%) This feature is'very important.

M2 :0 (46b) At the plane A -A, looking to the left, the pedanc'e Z1. is p, R (5) Z "c0's'BL+i'sin 16L ORGZ =0- (46c) -U 13+ cos BD-l-z' ZL sin BL 1 6 C 0 (4 d) which reduces to a more'eonvenientfonn +1? cos 25L+ I Z, r Y-Q-Y WW 0 (466) ZFZkI ("0 Rh 2 a A (a) 17; 25H

where a: and we are functions of frequency, and R is practically independent of frequency for Instead of the inequalities of (48) it is convenient to write small frequency changes A near but it is apparent that the solution :of the simultaneous 1i Equations 46 is impractical. However, consideration of the desired result in view of-the circuit of R Fig. 4 permits certain assumptions to be made Where which simplify the solution.

In Figure 4 let L=0, and let R be the load rel and sistance directly, (or some transformedioad re R sistance). By connecting in series with R a re- Thus t is the Q ratio f the tr nsformed actance m which is a function of frequency, one ance to the untransformed impedanca element of a parallel (referred to a plane through l iresonant circuit is provided. The other bfiei (5,1) element is Rs-l-izce. Formaximum rate of phase 1912+m2 change with frequency at AA, impedance where U 1. The product Ut may be maximized Retix and R6+ii36 should have the highest poswhere the line length fiLwill become the variable. sible Q values. By using a shorted section-of 10W Considering frequency -changesof the form attenuation line it is seen that f=f(1+a) zszixfi (47); where f0 is the initial frequency, 8 may be either positive or negative, and 5 1. Then The branch Z contains the load resistance R 2 Which limits the upper value for :1: since, if x is 2 (52) too large, the resonant resistance at AA will be R2 Using Equations 54 and 55 in 51, it is seen that Since it is desirable to make the inequalities of (48) as great as possible, it follows that the conditions which make the product Ut a maximum are desirable. The conditions which make U and t reach their maximum values independently should be checked to be sure that the required conditions are not opposing.

From Equations 56 and 50 The roots are 3 212-1 cos2BL=0 L=Q 4 1r (63) where n is any integer and tan 2BL= x and to fulfill Equation 52 tan 25L 0 and 6L= 2 n is any integer.

12 The conditions to be investigated occur, therefore, at

cos 2BL=0 sin 25L: 1

cos 2BL==0 sin 2BL= 1 cos 26L: 1

sin 25L=0 and cos 25L 1 sin 213L=0 In each case Rt and an may be obtained by the use of Equation 49 and these quantities may be compared with R and a: respectively. In each case assume k Then for the first condition, Equation 66 3 Z =R+i$= k 3 Rg= x%' and in Zk The initial impedance Z was Z=R+ix=Z +ix so that the quantities U, t,

and

JEL amay be compared "i l I;

i R x 2Z (73) Q== 4 n i Qt k The interesting result is that Q2 7 QF; 0

and at the same time 2 2 'v z l- R g It has been assumed that Q 1, so if Z=R+ia: is parallel resonated with a reactance :c'Ea: the resonant resistance is Rres=$Q (77) is parallel resonated with a reactance xr'a-xr, the resonant resistance is at the same timethe parallel resonant resistance has been decreased from ros 2 For the second condition of Equation R to The "initial (Z=R+ix inparallel with i:v) resonant'resistance is Apparently the only difference is that the ance are changes sign.

For the third condition of Equation 68 reactor t ond tion. o hin s e e e sed or gained ty tlieftrarisformation. For the fourth d ii eo Equeii fi l Continuing as before {B a; .-RTZ;. (9.5) Qi= (96) Theinitial z=a+z i in parallel'with i.'1:) resonant 'resistanceis Rres=i11Q- (99) while the transformed. parallel resonant. resistance is IBS F Therefore itmay be concluded that the first two conditions are identi'cal -excpt for change of sign or the reactance as and both are very useful.- Conditiori three 'isoi "no value and condition four The physical circuit configuration which will" may be done withsections of transmission lines or with sectionso'f wave guides having the necessary modifications. The circuit of Figure 5 will provide the arrangement of; Figure 4,to the leit; of A-A. The circuit is composed of R, the shorted length of line L2 and the line L. However, if the reactance x, where a1=Zetan 5L2, is large as compared to R, as is necessary, it will be diflicult to deliver sufificient power to the resistance Thereiorie, it is convenientlto substitut "the circuit of "Figure 6. The line L2 initially is selected to' be approximately n r wave-" lengths long and the we) elength is varied from A to 1+6) where it j is assumed that. 6 1'. Thus gleam-+11: (101) and (3L2 changes in I the following manner pLz=(n1r+) (1+5). (-102) The resistance. Rs, where Rs- 0, .is insertedto provide. a decoupled re onator. The equivalent;

circuit,,usingisectionsyofwave guides, is shown in that the, resonator above Rs, but including Rs,

in Figure 6 reduces to the circuit ofFigure 9.

In similar fashion the effect of the cut-off window between L3 and the resonator L2 in Fig ure 7 also must be determined. It is useful to introduce the auxiliary circuit of Figure 10 for this purpose. It may be shown that the resonator. above the cut-01f window, but including the window, in Figure '7 reduces to the circuit of Figure 11.

Apparently it is not generally appreciated that the resonators of Figure 9 or Figure 11 when viewed from R5 or the cut-off coupling window respectively, or at a plane n11- removed may be made to operate either as series type or parallel type resonators.

In the waveguide case this is efiected by choice of window size as compared to that window size which matches the resonator to the wave guide. This fact is especially important. For simplicity it may be assumedthat the lines to the right ofxn in Figure 9 and to the right. of; window aw in Figure 11 have no attenuation. Then for series type operation as viewed from Zm and Zn: re-

15 16 spectively, an. and cut-on guide BcLc, which is of cut-off guide Zkc must be a negative imaginary represented in Figure 11 by .Lw, may be omitted so that for all practical purposes. At resonance in Figz i z (107) ure 9 and Figure 11, [3L2 will always be 7111'. In T both cases the resonators will display all the char- 5 3:2fi gfi a gfi fsigig ggzgg g fs of acteristics of series resonators, and at resonance the resonant resistance will be low and approach Q 0 as R 0. Z 7 SIDMBOLC) 108 In many cases it is desirable to have Z1. and Zw W L @Sinhw L in Figures 9 and 11 respectively, exhibit the char- 10 Z acteristics of parallel resonators with their charwhich reduces to acteristic high resonant resistance. This may be 7 7 if 1 me 1 a (an) +i(t+)anh aLc In Figure 8 a line of characteristic 1mpedance ZW: Zk 1 Zk is shunted with a resistance Rs 0, and the 15 cc) termination Zk is provided, as shown. Then, #2 (109 i H tan tan l 1 Zk+RS and for [30110 small tang l 1 (Bc c) (H i ;)(B L 103 M6 2 110 which for Rs- 0 reduces to if %Z+W RS For the special case where 5Lc l, =Z -=z 1 104 ZL n 2 Zfiw ZW=1+1Q+ at. (111) Disregarding t 1 part of Equation 104, Since so that it appears that the thin cut-off section of that it is a term which will afiect only the Q, the W v guide S rves as a lumped reactance ix, discontinuity provided by Rs is equivalent to the Whlch 1S reactance in. in Figure 9. 1

The reason for introducing in Equation 101 w= (u+z)flc c (112) is apparent. If is large enough so that the input reactance of {3L2 is negative, the arrangement of Figure 9 is obtained where in and the negative reactance of line fiLz, which is iZk tan 5L2, are parallel resonated. The line ,BLZ is never mr at resonance, but instead is always in the second or Again in Equation 101 the value of 5 is chosen so that BLz in Figure 11 is in the second or fourth quadrant. The reactance ixw is resonated with the negative reactance Z1; tan {3L2 at the desired frequency. The resonant resistance is a funcfourth quadrants. The impedance Zm in Figure tion of 9 accordingly may be a large resistance at reso- 1; a ne nance and has all the characteristics of a parallel Z tan {3L resonator when viewed mto the left of am.

The same situation exists when wave guides are used with a thin cut-off window. In Figure 10 sa a thin section of cut-off guide is terminated in a Z,. tan 5L section of guide of characteristic impedance Z1; At any one frequency the magnitude of the which is terminated in turn by this case allel resonance resistance is controlled by proper the propagation constant of the section cut-ofi ghoice of PM Be, he and 5L1 Again at resonance and increases with increasing guide is g m vzigf 2 y (105) Since, for some applications, it may be advan- 2a tageous to operate the resonators of Figures 9 and Where M is the free space Wavelength and a is 11 as series resonators, the conditions for this the width of the guide As usual, beyond operation must be determined. The right hand off termination in each case becomes R O.

M The impedance Zm must be determined. This 1 t1me the line is m long initially at resonance, and changes from War to I'L1r(1+5) as the wavelength so that Equ 105 becomes in the guide is changed. Again Rs 1, and

27! X 2 1= e. (106) fi=m-fi The characteristic impedance of the section Then B n1r5 7Z1r5 (m5 n1r8 aR 2 Zma-z/ M +3111 m)[ 7; v v 00s (mr-@)+l: in 1 (1M) And when Zm is connected in parallel with Rs,

fig 7L1r5) (7115)] (7115) 1L7r5 (IRS 2 R Z |:cos mr +s1n +is1n cos mr -11} Miami? 17 Mme symmetrical case a -1, andn evenxmciua tion 115 reduces to 1M7: Z 'nmi g 2R, (1 +5) 2 Z nmS 2 QU i and is for 6 1 As fiofiid liexiict'ed "2" has the characteristic form of impedance yariatiqn of a resonator, as w e l qm qem e qea e ii ee 7,, W, t asiutien $91. is co e itefii? resonator and if the equivalent "Q seizpre's'sd as in; pd z, bm-r. r I4 -i, r then Equation T05 converts to the characteristic form and the phase change '01 z' tvith'irequeney is proportional to Qt as wouldbeexpected.

Similarly, for Figure 11, BL; will be mat resonance and change to n1r(1+8) with changes in wavelength in.the guide. The termination for the thin cut-ofi guide is 1+1?) t'an mow (12) Since the impedance change near resonance is to he. us d. 921iresmeeqx.sq tmlcnemi ea itie e ble st peratet eser ty re eee ea 19 I off. Accordingly, the changer \v av glegig h ln gl rectangular guide (also used as a resonator 111 this application because 1of convenience) A either with frequency or its inverse X0, the free space wavelength is important. V The guidehas cross "ectiox'i a e'ihd d 'l5; The wavelength in the guide is Then \ 1. (id) m -(a) Fonstaztdam, x-lbandl uidezaFl-fiq in hee 1 3 att9-3l0 megacycles per second 7\u=1.27 inches, so that where X0 is the free space vvavelength, b a, and the special case where c '-b'.

X111 te ieo ma iee admi anc eetra clet to 2:0 for the iert ized admittance extrapolated to 2:0 fer in; right leg. Z 0. I

Y2 is the normalized adri'iittance extrapolated toy=b.for;the vertical-leg. .y b. Wl. .1

U 'Yir--..Ya. -1 fora travelling Wave prop gated in tl1el+Z direction. 1 l.

Yi=Y3r-..l fora travelling wave propagated in the .-l-Z direction. l c 1 a For the circuit configuration'of .Fi'gure 6; Yi'; Y2; and Y3 are related by the following two equations; 1

th .wa lengm f. t

m r cur ard X-band wave giii Considering the case where vvave propagation i S fiIOIljl thekleft where the 'rtical branch has an admittanE'mYg} ,afid w Lifl uthe right 11am: branch has a matched termination,

Y3=1 and Equation 128" Y3:

Y "2.'+4;SYZ(2B1YQ.73'5) It is sonretinies easientp use a rationalized form of Equation 131. If Y2 is of the form Y2=y(cos 0+2 sin 0) In Figure 'I the resonant resistance of the resonator'may be expressed in terms of the characteristic impedance of the line Lo and may be considered as a termination for L3. The impedance of the resonator off resonance as a termination for L3 should be considered to determine the rate of change of phase angle and reactance with frequency. It is convenient to consider the resonant resistance and impedance values Q above and below the resonant frequency. The resonant resistance is aoZk where 21: is the characteristic impedance of L3 and aoZr is either greater than, or less than Zr, as has been shown. The impedance at a frequency Q higher than the resonant frequency will be and the impedance at a frequency Q lower than the resonant frequency will be To complete the frequency control circuit of Figure 4, it is only necessary to consider various terminations for L3 in Figure '7 which involve various values of ao, and. the transforming action of L3. This terminating admittance is the Y: of Equation 131. The admittance Y1 is then the termination for line L in Figure 4. Line L transforms Y1 to a new admittance at the plane AA. The corresponding impedance at AA is then parallel resonated with the reactance provided by line L1.

This final resonator is then connected directly to the oscillator, or to the oscillator through a coupling line or circuit.

It is necessary first to determine the line length L3 'in Figure '7 which will give maximum rate of phase change at the junction with line L, all for a change in phase at the resonator, which is then the termination for L3. The resonator termination in terms of Zr is aoZk. At resonance 110 is a real positive number, and off resonance it is complex with a positive real part, so that Accordingly, the normalized input impedance of line L3 as viewed from line L is 71020. 58 11 (7,1 G2 tan 1 2a; tan BL (a; +11 tan 5L (135) and the phase angle is measured by a (ltan BLQ-l-(l-aF-a?) tan 3L3 2.- 2 (lg COS Sill 8L;

1 P-w al 20 To obtain the maximum rate of change of P with ,BLsandaz I a P OBL and 2. If the resonator termination on L3 (Figure 7) operates as a series resonant circuit ao 1 and L2=n1r initially, then from Equation n I I 2 2 2 Condition 1 is preferred since the high ratio, and necessarily low attenuation line transformer which is automatically incorported in condition 2 is avoided. However, if extreme care is taken to make the line transformer very low loss, condition 2 is also capable of providing good results. Since condition 1 is the preferred condition, it may be assumed that in Figure 7 3L2 (at resonanceh mr, pL3==n1r but it should be understood that the alternative condition may be substituted, although the results then are likely to be poorer mainly because of the difiiculty in making the transformer good enough.

All that remains is to determine line length L in Figure 4. Equations 66, 67, 68, and 69 which result in Equations '76, '77, 83, 84, 90, 91, 9'7, and 98 indicates that ,BL should be either The better condition may be determined. For various resonator terminations (ZOZk for line L2, where (lo 1, 8L2=1L1n Equations 131 or 132 provide the values of Y1 for the various indicated conditions of Table 1. Conditions at resonance and ofi resonance by /2Q in frequency are shown.

Comparing the initial phase angle of the resonator, Y2, and the phase angle of the control impedance Z1, it is evident that the resonance characteristic of Z1 is not symmetrical about the resonant frequency, but becomes approximately so in the region Y2=0.2 to 0.1. Also, the phase angle change of the loaded resonator Z1 in the same region Y ==0.2 to 0.1 is equal to, or greater than, the original change in. phase angle of Y2.

It is possible to improve the symmetry about resonance by operating with flL3E13 30 for which Y1=1, but only at the expense of reduced rate of change of phase angle of Z1. Use of an iris to provide a lumped reactance in {9L3 to provide the equivalent of operating {3L3 at length ,sL3=nr+13 30', is possible.

The entire control network may be considered as a network made up of passive elements, and the insertion loss, defined in usual fashion, may then be computed. For the insertion loss to be significant it is necessary for the controlled oscillator to operate on the same point on its characteristic, and at the same frequency, with and without stabilizer.

The maximum power output for the oscillator, with potential 6, working into a matched termination R is Table III Resonator terminations llnZk for line L1 in Figure 7.

Y2 (normalized)= Power in Matched Termination Insertion Loss Percent Reference power with no stabilizer is .25 e.

A good operating region extends from about ao=3 to about ao=10. The resonance characteristic is not quite symmetrical about the resonance frequency, but the average loaded Q for Z1 for ao=10 is about .72 times the unloaded Q of the resonator out on line L3. If the Q of the resonator is 5,000 to 10,000 initially, stabilization to fractions of 1 megacycle per second in 10,000 megawas? cycles per second for reasonable variations in operating parameters is feasible. For (10:10 the insertion loss is 55%. The average loaded Q for the synthetic resonator Z1, for an=5, is about one times the unloaded Q of the initial resonator and the resonance characteristic again is not quite symmetrical about the resonance frequency. At ao=5 the insertion loss is 38%.

The performance does not change rapidly for values of a0 between about three and ten. For a value of 110:3, the insertion loss is about 23%.

The final choice of a0 is a compromise. Operation is somewhat better for a1 ==5 to Ger-10, but not :24?v tremendously better than for ao=3. Therefore, any value of a0 betweenabout 3 and 10 is satisfactory.

The case where should be considered. 'For the same various values of an, take as terminations for line L values of from Table I. For simplicity, consider the case where n=1. It is evident that the line transforms to Z1, which is (normalized) Zt=Y1 (152) As before, corresponding values of Z1, the control impedance may be'computed from Equation 150. The results are shown in Table IV. Comparison of phase angles for Y2 at resonance and at frequencies C,)above and below resonance, with the corresponding phase angles of Z1, indicates that the rate of phase angle change with frequency is much slower for Z1 than for Y2. Also conditions are much worseithan those in Table 11 where L was Table IV Resonator terminations 1102,. for line L1 in Figure 7. 2n 1 BI4==mr Y2 (normalized)-=- 10 Y: (normalized) Z, (normalized) Z 02 v 0743-1-12 1240 2702i .02 (1+5) 0847+i. 1365 257-L 1475) Z), 02 1-1 0640+i. 095s 206+i. 111) z. 04 0955+1'. 1085 ZZZZI: .04 (l-H) l1170+i. 148 278-1'. 181)Z; .04 (1- -2') 0792-1-11 0848 1655+i. 0818) Z1. 10 1520+1'. 0809 1957.1: 10 (l-H) 1506+i.165 320-1'. 116) Z;: 10 (1-2') 1214- 1-11 0127 1175+i. 389) Z 0 239+i. 0793 2722 20 (1+1) 298+z'. 214 439-1: 122 z. 20 (l-i) 232-4. 0735 184+i. 00525) Z1. 1. 0 564-1'. 0803 576Zk 1. 0 El-I-t) 538+i. 565 438+i. 0376) Z]: 1. 0 1-!) 785-1. 2155 828+i. 0619) Z 5- 0 868-1'. 164 895Zk 5. 0 (1+1) 937-4. 1098 874+i. 0245) Z 5. 0 (1-1) 909-11 323 (1. 14+1'. 088) Z):

Equations 68 which lead to the results of Equations and 91 indicate that a line BL=TL1r will not give good results. This prediction may be checked by numerical calculations. For

BL: (2n- 1) 1r and the special case where n=1 which is the normalized value of Zt. The results are shown in Table V. As predicted by the general analysis, the rate of phase angle change of Z1 with frequency departures above and below the resonant frequency by /2Q is less than the rate of phase angle change of Y2, and much poorer than the results shown in Table II. Accordingly. the line 5L should be in length. As indicated heretofore, n should be greater than unity to utilize the greater phase sensitivity of a longer line. Also, it is advisable to have the wave guide operate fairly near cut oil so that the rate of change of wavelength in the guide is greater than the rate of change of frequency or of free space wavelength.

Table V Resonator termination a Z for line L3 in Figure 7.

g =77/lr 8Ls=fl o 1 Y (normalized) Y: (normalized) Z; (normalized) 7 02 3. 55-15. )8 13. 46 1 02 (1+1) 3. 29-15 31 (11. 7-13. 67 Zk 02 (1-1') 4. 83-17. 23 (13. +i9. 32)Z;, 04 4. 57i5. 20 10. 5Z1. 04 (1-l-i) 3. 29-14. 17 (7. 70-14. 98) Zk .04 (1-i) 5. 89-i6. 31 (11. 65+1'5. 69)Zk .10 5. 24-12. 79 6. 70Zk l0 (1+i) 3. 03-13. 33 (4. 91-21. 875) Z), (1-i) 8. 14-1-1. 853 (5. 38+i1. 586) Z). .20 3. 77-il. 253 4-19Zk 20 (1+1) 2. 23-21 60 (2. S31'. 823) Z), 20 (1-1') 3. 92+il. 24 (3. 00+i. 086) Z). l. 0 l. 735+i. 247 1. 835Zk 1. 0 (1+1) 883-i. 928 760+z'. 0988) Z]. l. 0 (1-1') 1. 186+i. 325 (1. 245-11 1315) Z1. 5. 0 1 112+i. 210 1. 155Zk 5. 0 (1+1') 1 055-l-i. 123 (l. 070+1 0427) Zk 5.0 (1-1') 976+i. 5475 (1. 031+1. 0555)Z1i Mn'rnon IV--COUPLING or STABILIZER T0 OSCILLATOR Any of the usual types of coupling to the oscillator may be used. In the case where the oscillator is a magnetron a particularly useful type of coupling is shown in Figure 15. A coupling loop, not shown, is placed in and tightly coupled to the magnetron cavity or cavities and connected to a concentric line. The outer conductor 5 of the concentric line is terminated in the lower wall 1 of the wave guide as shown. The inner conductor 9 extends up into the guide a length Le.- As before, the width of the guide is a and the height is b. The coupling loop in the magnetron cavity, length of concentric line and antenna of length La Will, in general, present an impedance which can be represented by a complex number of the form Zint=Rint+iSmnt Zint=Rint (155 The greatest change in operating frequency of the magnetron cavity results when the current in the coupled concentric line 5, 9 goes through its maximum value. This condition should occur if the radiation resistance of the antenna La goes through zer This condition results, in turn, if the guide impedance in the plane AA goes through zero.

If the antenna radiation resistance does become zero, or approximately zero, the power output or the magnetron Will be very adversely affected. Therefore the radiation resistance chosen must be a compromise between very low value which would give remarkable stabilization, and a somewhat higher value which will still provide acceptable stabilization.

Inspection of Table II, especially in the recommendedregion ao=3 to 5, indicates that this second condition maybe met. The problem may be considered from either the point of view of the antenna La and the efiect thereon of the 5 impedance Z1 coupled to it by the guide, or, from the Point of view of the impedance Z1 and the effect thereon of the antenna coupled to it. In either case, by proper choice of h in Figure the reactancewm must be cancelled out so that only Rint remains. Also, in either case th coupling factor 15a of .theantenna La. to the guide will appear. as follows:

2 Isa- Sin where a, b, and d are indicated in Figure 15.

If standard X-band wave guide, La=)\/4: at the operating frequency 9210 megacycles per second, and d/a=% are employed, then ka=2(.'195) sin 1r/2=1.265 (157) In the first instance, the antenna of resistance Rlnt has connected to it the external impedance Z1, but the coupling factor ks. enters to make the equivalent external impedance kaZ1=1.265Z1.

. In the second instance, the impedance Z1 has connected toit the resistance Rlnt but again the coupling factor ka enters to make the equivalent resistance will be propagated. The initial electric vector intensity is A, and 'y is the propagation constant. No other modes will be propagated. If other modes were propagated the same analysis would hold provided the integrations are changed to accommodate the new E and H distributions. For 3 cm. waves, the standard 1" x /2" wave guide fulfills the conditions A )l e e" The length of resonator for Z= \2 is L= ./22b. Also aE2b, thus the end area A1 is Assuming a. uniform substance for the walls, it follows that the respective end and side resistances are R1=Ro (162) R2=2Ru (163) 76 Considering the ends first, the current distri- 7 27' bution in the y direction is sinusoidal, and the average current along y is "JFgl ma (166) and the energy lossinthe sides is so that the ratio of the energy loss in the ends to that in the sides is If the Q of a resonator is defined as Q Energy stored in resonator Energy loss in resonator then the Q of astandard half wave resonator is Ill J Qo/z) 3 (169) where J3 is the energy stored, and J4-i$ the energy loss, in the resonator. e

For L=)\/2, J4 will be J1+J2 so that from Equation 169 1 V Quay- (170) For a resonator long the Q becomes 7 (n 1).] 1 J Q 3 j- (1 1) where the primes place the energy on a per X/2 section basis.

so that the improvement in going from n==1 to n= is The analysis heretofore has assumed a uniform wall material. Since the ends involve a soldering or welding operation, it probably is more accurate to assume the end wall resistance is about equal to the side wall resistance. Thus, the end wall energy loss is J where and the side wall energy loss is Jfi=1 mR0 (176) The ratio of energy loss in end walls to energy loss in side walls is r, 4I maX 1: 2 (177) Therefore,

2J Qu/2)=7: (178) where Jr is the energy stored in the length M2. For

where the primes again denote a per M2 section basis. 7

For the limiting case n Q(co) 7? (180) so that the improvement in Q in going from n=1 to n: is

Equations 174 and 181 show that the Q of a resonator does not increase linearly with the number of half wavelengths of length for an assumed reasonable loss distribution.

This analysis holds only when end wall resistance and side wall resistances are assumed to approach 0.

Equations 172 and 179 indicate that the rate of improvement obtained by adding half wave sections to a resonator beyond 3 or 4 becomes negligible. The same equations, however, indicate that if the ratio of end wall losses to side wall losses is high or higher than that assumed, it may be desirable to add half wave sections beyond this 3 or 4 value.

A first practical circuit configuration of the invention, adapted to waveguide construction, is illustrated in Figures 16 and 17.

An ultra-high frequency generator comprising a conventional magnetron ll, of which the magnetric structure is omitted for the sake of simplicity, is coupled to a transmission waveguide system l3 which is coupled toa load, not shown. The output coupling line I2 of the magnetron H includes a coupling loop, not shown, which is closely coupled to one or more of the magnetron resonant anode cavities. The end of the magnetron output line 12, remote from the magnetron proper, is terminated in a short antenna 15 which extends into the waveguide transmission system l3. Reactance in the magnetron output line I2 is cancelled by means of a reactive stub I! opening into the waveguide transmission iine I3 adjacent the magnetron antenna l5, whereby the magnetron output is made substantially resistive at the plane AA of the antenna in the waveguide system. The load is matched approximately to the waveguide transmission system l3 by means of a first conventional tuning screw l9 extending through the waveguide wall adjacent the load connection.

The stabilizing network includes a closed waveguide reactive high Q stub 2| extending normally from and opening into the transmission linet3 at a point. intermediate-the; lcadfiami a generation The reactance of'thcicontizolzstubphi is. adjustable by means of a. second tuning-retreat 23; The degree of coupling: from: thocontrol stub Unto. the transmission line I3:is,=dctermi iedrby"% coupling aperture device 25 in the tuning stub waveguide.adjacent.thepoint;whcrelitopens into thetransmisison waveguide lid. The. plane B.'-B of" the control stub 2.1 is. selected tot beisome mi l tiple of one-half wavelength. plus. or-.:m-i:nus. /9 wavelength from the IpIaneaATA. 011 the-masnetron antenna. Thus, by meansof: a thirdiuning screw 21 extending into the transmission; waveguide It intermediate the planes- Bi -:3, and Al-71A, the efiiective transformation of the. impedance of the: controls stubi Zlprovided: by the impedance transfiormer H3, comprising the portion; ofiithe waveguide system l3,- intcrmediate; the; planes AsfiAandB-B:, be adjusted; at the/plane Aw- Awhich is eflectively the: resistive termina. tion .oithe magnetron antenna. The: reactive stub 2| and secondituningscrew 23;: maybe. cons siiiered; to-be a resonator only as; seenvirom the clzunling aperture 25. At the plane-A-fl-A of; the magnetron, antenna, the. combination: ot the stale and tuning. screw appear as an impedance.

4%.. fourth tuning. screw- 2-9. extending intol-the transmission waveguide 13. on the oppositeside ottheplane A-A from the. plane-1.3+Bj of the centrole stub. it provides means whereby the transiormed impedance of thecontrolv stub-may be; resonated in. the plane. A -A. at the ou put. ire- --quency of the generator I l.

The char cteristics o the contrct 21 and the second tu ee r w 2:3: coupled; th retoiare selected to have. relatively hi h reactants with high a Q value. asconventionalconstrue: tion' will permit. Thus, by meansgoi' til'litlime pedance transformation provided-1 y hes xensformer- M betweenv the planfist B--B. and the resultant reactants atthe plaudits-A. d othe control stub 2.! will be substantially lower. than the; reactance of the control stuloitseli and Will ve a, substantially higher Q value... The transformed reactance at. the; plane Ae A thus may be resonated by means of, the icurth tuning screw- 29 efiectivelyto. provide. an e tremely hi h "Q resonator at. the. plan A-A, which willbe e tiv ly connected in shun with the resonan cavity anode. cithe ma netron it through. the coupling. line which includes the antenna, ii,

The characteristics. of Waveguide T junctions are well known and are discussed in detail in the literature. Similarly, the reactive ellccts oi tuning stubs coupled. into waveguide transmission systems are well, known ,as is the specific structure of such reactive devices. Detailedconstruction and theoretical consideration of" appropriate tuning screws is included in the copendingapplication of Vernon D. Landon, Serial No, 5083229, filed October 29, 1943; Patent Numbe-r $427107; which is assigned to thesame assigneeas the instant application.

In operation, the magnetron H is 'adjusted 'by any conventional frequency adjusting means included there-with to provide the desired output frequency. The first tuning screw t9: is adjusted toprovide adjustment of the load coupling impedance to. match approximately the load to the transmission waveguide l3. and'to permit nearly symmetrical tuning on either'side of resonance -monance, asvviewed from the aperture 2!, at

thlnopenoting; frequency; as may be... determi d partially by initial calcu a ons. The iourtht: insrscrew 2.9 thellziszafill ll tfi toresona e theccn: trot imp dance at. the. planeA-A oi. t e. mas nettoh. antenna, next, the third tunin screw 2ft adjusted tolvary'theimpedance, transforma-.. tion at. the plane; A..A oi h ma netr n an:- tenna topobtainl thehishest prac icable Q va ue. not the control; impedance. in; view f; th res s ive load. thus. placed up n the ma n t on. as, ex: plained; detail heretoforei The fourth, tuningv screw is. again. adjusted to: resonate the. control; impedance. more. accurately t the s illatoro. but frequcncm. nec ssa t e firs tunin screw. this again adjusted. tomat h. the load: to the waveguide transmission system 13;.

tiscassumedthat the. reactive stub ll adiacentth magnetr n an enna I5.- hasv be n pro:- ula d; or presetv to p vide? the d ir d cans collation of reactance in the magnetron output line to the antenna l5,. If; necessary, an adjustable shorting. plug 31 may be included in the reactive, stub I1 to provide adjustment of the reactantsv thereof.

In Figure18 a preferred circuit configuration includes; a, cylindrical high Q control reactance 2l:-w-hi.chi c d s a tun n pi on 33, the 1o.ns tudinatx position of. which. may be adjusted by means, of a micrometer screw 35. The control reactor 21" is. coupled; to a, T junctionv 31 which extends; from the. narrow side of the waveguide transmission. system i3. A second T junction 35 extendin from the. pposi e narrow sideof the waveguide. system i3 includes; a third tuning screw: '21 which is employed to vary the coupling of the control impedance 2|" to the impedance transformer M; The first tuning screw I 9 is operable through the transmission waveguide wall intermediate the plane B..B of the control impedance and a load, not shown. The. mag? tic-tron generator has been; omitted for the sake of simplicity.

The operation and adjustment of the system is-similar to the device described by reference to Figures 16: and; 171 However, the cylindrical construction of the-control: impedance 2! permits. a h s-her Q to. be obtained from this element with finer adjustment of the control impedance value.

The higher Q control impedance results usually in higher values of resonant resistance and higher reactances atv the coupling aperture 25 slightly off resonance. Thiswould result in an unfavorable situation ifused in the arrangement of Fig. 116. and Fig. 17 in which waveguide branches t3" and 41 are approximately in series as far as thesimpedance transformer I4 is concerned, since under these conditions the power delivered to the load'would be small.

Forthis. reason the T junction of the type shown in Fig. 18, in which the Waveguide branches l3 and 31 (with the additional reactance of, the stub 3:9) are approximately in parallel, is used with a high Q control impedance 2], since the high impedances are then in parallel with the useful load. Since the impedance transformation and resonating is otherwise similar to. that described in Figures 16 and 17, the elfective control impedance Q at the plane A=.-.A is substantially improved, thereby providing greater stabilization of the generator frequency,

as indicated heretofore.

Thus the invention disclosed and explained theoretically herein comprises. several embodiments and modifications of a frequency stabilizer for wave generators, or of synthetic resonators" wherein an impedance represented by a complex number is selected, transformed to a new impedance with a higher Q and lower absolute value, and then parallel resonated with another reactance having opposite sign; This synthetic control resonator is used to stabilize the frequency of the generator. Circuits having rapid rates of change of phase angle with frequency are employed, and critical optimum line lengths are determined to provide a practical circuit configuration. The instant invention appears to differ from prior art devices wherein a high Q control is used directly, or wherein the elements of a resonator are combined first and then transformed to new values.

It should be understood that several sections of the circuit configuration described may be cascaded, but circuit adjustment may become very diiiicult.

I claim as my invention:

1. The method of employing a control impedance for stabilizing the frequency of a signal generator comprising the steps of transforming the value of said impedance to a lower impedance value having a relatively higher Q, resonating said transformed impedance substantially to 'said generator frequency, and shunting said generator by said resonated transformed impedance.

2. The method of employing a control impedance for stabilizing the frequency of a signal generator comprising the steps of transforming the value of said impedance'to a lower impedance value having a relatively higher Q, resonating said transformed impedance substantially to said generator frequency, shunting said generator by said resonated transformed impedance, and cancelling normal coupling reactance between said generator and said resonated transformed impedance.

3. The method of utilizing a control impedance for stabilizing the frequency of a signal generator coupled to a load comprising the steps of cancelling normal coupling reactance from said generator, transforming the value of said impedance to a lower impedance value having a relatively higher Q, resonating said transformed impedance substantially to said generator frequency, and shunting said reactance cancelled generator coupling by said resonated transformed impedance.

4. The method of utilizing a control impedance for stabilizing the frequency of a signal generator coupled to a load comprising the steps of cancelling normal coupling reactance from said generator, transforming the value of said impedance to a lower impedance value having a relatively higher Q, resonating said transformed impedance substantially to said generator frequency, shunting said reactance cancelled generator coupling by said resonated transformed impedance and coupling said load to said generator through said impedance transformation.

5. The method of utilizing a control impedance for stabilizing the frequency of a signal generator coupled to a load comprising the steps of cancelling normal coupling reactance from said generator, transforming the value of said impedance to a lower impedance value having a relatively higher Q, resonating said transformed impedance substantially to said generator frequency, shunting said reactance cancelled generator coupling by said resonated transformed impedance, coupling said load to said generator through said impedance transformation and matching said load to said load coupling.

6. The method of effectively synthesizing a high Q resonant network including an impedance element comprising the steps of transforming the impedance value of said element to a lower impedance value having a relatively higher Q value, and resonating said transformed impedance.

7. A high Q resonant network including a high Q impedance element, means for transforming the impedance value of said element to a lower impedance'value having a relatively higher Q value, and reactive means connected to said transforming means for resonating said transformed impedance.

8. Apparatus for stabilizing the frequency of a signal generator, including a high Q control impedance element, means for effectively transforming said impedance to a lower impedance having a relatively higher Q value, reactive means resonating said transformed impedance substantially to said generator frequency, and means for connecting said resonated transformed impedance in shunt with said generator.

9. Apparatus for stabilizing the frequency of a signal generator having a frequency determining resonant element, including a high Q control impedance element, means for effectively transforming said impedance to a lower impedance having a relatively higher Q value, reactive means resonating said transformed impedance substantially to said generator frequency, and means for connecting said resonated transformed impedance in shunt with said generator resonant element.

10. Apparatus for stabilizing the frequency of a signal generator having a frequency determining resonant element, including a load coupled to said generator, a high Q control impedance element, means for effectively transforming said impedance to a lower impedance having a relatively higher Q value, reactive means resonating said transformed impedance substantially to said generator frequency, and means for connecting said resonated transformed impedance in shunt with said generator resonant element and said load.

11. Apparatus for stabilizing the frequency of a signal generator having a frequency determining resonant element, including a load, a transmission line coupling said generator resonant element to said load, a high Q control impedance element coupled to said line, an impedance transformer connected to said control element for providing an effectively lower impedance and a relatively higher Q value, means for providing a resistive termination of said generator at a predetermined point on said line, and reactive means for resonating said transformed control impedance to said generator frequency at said point on said line.

12. Apparatus for stabilizing the frequency of a signal generator having a frequency determining resonant element, including a load, a transmission line coupling said generator resonant element to said load, a high Q control impedance element coupled to said line, an impedance transformer interposed in said line between said control impedance element and said generator for providing an effectively lower impedance and a relatively higher Q value, means for providing a resistive termination of said generator at a predetermined point on said line, and reactive means for resonating said transformed control impedance to said generator frequency at said point on said line.

13. Apparatus as described in claim 12 includ- 33 ing adjustable means for matching the impedance of said load to said transmission line.

14. Apparatus for stabilizing the frequency of a signal generator having a frequency determining resonant element, including a load, a transmission waveguide coupling said generator resonant element to said load, a high Q adjustable control impedance element coupled to said waveguide, a section of said waveguide providing an impedance transformer interposed between said control impedance element and said generator for providing an effectively lower impedance and a relatively higher Q value, means for providing a resistive termination of said generator at a predetermined point on said waveguide, and reactive means for resonating said transformed control impedance to said generator frequency at said point on said waveguide.

15. Apparatus for stabilizing the frequency of a signal generator having a frequency determining cavity resonator, including a load, a transmission waveguide coupling said general cavity resonator to said load, a high Q control reactive cavity element coupled to said wave guide, a section of said wave guide providing an impedance transformer interposed between said control reactive cavity element and said generator for providing an effectively lower impedance and a relatively hgiher Q value, means for providing a resistive termination of said generator at a predetermined point on said wave guide, and reactive means for resonating said transformed control impedance to said generator frequency at said point on said wave guide.

16. Apparatus for stabilizing the frequency of a signal generator having a frequency determining cavity resonator, including a load, a transmission wave guide coupling said generator cavity resonator to said load, a second waveguide forming a T junction with said transmission waveguide and comprising a high Q control reactive cavity element coupled to said wave guide, a section of said wave guide providing an impedance transformer interposed between said control reactive cavity element and said generator for providing an effectively lower impedance and a relatively higher Q value, means for providing a resistive termination of said generator at a predetermined point on said wave guide, and reactive means for resonating said transformed control impedance to said generator frequency at said point on said wave guide.

17. Apparatus for stabilizing the frequency of a signal generator having a frequency determining cavity resonator, including a load, a transmission Wave guide coupling said generator cavity resonator to said load, a T junction in said wave guide, a cylindrical high Q control reactive cavity element of adjustable volume coupled through said junction to said wave guide, a section of said wave guide providing an impedance transformer interposed between said control reactive cavity element and said generator for providing an effectively lower impedance and a relatively higher Q value, means for providing a resistive termination of said generator at a predetermined point on said wave guide, and reactive means for resonatin said transformed control impedance to said generator frequency at said point on said wave guide.

LOWELL E. NORTON.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 2,088,461 Briggs June 27, 1937 2,245,627 Varian June 1'7, 1941 2,276,879 Rote Mar. 17, 1942 2,373,233 Dow Apr. 10, 1945 2,404,832 Espley July 30, 1946 2,416,080 Bailey Feb. 18, 1947 OTHER REFERENCES Practical Analysis of Ultra High Frequency, by Meagher and Markley, RCA Service Company, Inc., Camden, N. J Aug. 1943. 

